- Piston Motion Basics -
Some Not-So-Obvious Facts
Figure 1
Figure 1 shows an end-view of the crankshaft, connecting rod and piston in an engine which has a 4.0 inch stroke. For purposes of this discussion, the extended centerline of the cylinder bore intersects the center of the crankshaft main bearing, and the wristpin is on the cylinder centerline (defined as zero wristpin offset).
The drawing shows the orientation of the parts when the piston is at the furthest extent of its upward (in this picture) travel, known as the top dead center (TDC) position. The furthest extent of the piston's downward (in this picture) travel is known as the bottom dead center (BDC) position.
In this picture, there are vertical scales alongside the piston and the crankshaft to show motion of both (in subsequent drawings).
The dashed horizontal lines are marker lines which project from the top edge of the piston and from the center of the crankpin.
Now suppose you rotated the crankshaft in that picture exactly 90°, which is 50% of the crankshaft rotation required to move the piston from TDC to BDC.
QUESTION: Would the piston have moved down the cylinder 50% of its stroke distance?
The answer is NO. In fact, it would have moved nearly 60% of the total stroke (as shown in the next two drawings). The 50% stroke point occurs somewhere around 80° after TDC.
Figure 2
The geometry of the crankshaft and connecting rod mechanism produces this dissymmetry of motion. It is interesting because it is the source of several interesting properties relating to the performance and longevity of a piston engine.
In the Figure 2 drawing the piston and rod have been removed, and the crankshaft has been rotated 90° past TDC. The drawing shows that the centerline of the crankpin has moved downward vertically 2.0 inches (half the stroke) and 2.0 inches horizontally to the left. Since the vertical component of the crankpin motion is 2.0 inches, it is clear that the piston must have traveled at least that amount. However, the horizontal component of the crankpin motion has caused the effective length of the rod (the length along the line of piston motion) to become less than the actual length. That apparent "shortening" of the rod because of the horizontal motion causes the additional downward piston motion.
Figure 3
In the Figure 3 sketch, the rod and piston have been re-installed on the crankshaft (90° past TDC). Note that the piston motion is distinctly greater than half the stroke.
When the crankshaft is in any position other than TDC or BDC, the axis of the connecting rod is no longer parallel to the centerline of the cylinder (the line along which the piston, wristpin and small end of the rod are constrained to move).
If you look at this view from the side, the length of the connecting rod appears to be shorter. In fact, the effective length of the rod at any point is the actual rod length multiplied by the cosine of the angle between the rod and the cylinder centerline.
Now, since the piston has already moved about 60% of the stroke during the first 90° of crank rotation, it stands to reason that during the next 90° of crank rotation (to BDC) the piston will only have to travel the remaining 40% of the stroke to reach BDC.
The reason is that as the crank rotates toward BDC, the crankpin also moves horizontally back toward the center of the cylinder and "restores" the effective length of the rod. That horizontal motion of the crankpin opposes the downward movement of the piston, subtracting from the half-stroke of vertical motion produced from 90° to BDC.
NOTE: All the calculations and explanations on this page and the next page assume zero piston pin offset. A non-zero offset will slightly alter the calculations, SLIGHTLY being the operative word.
